-8x+14=2x(4x-7)

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Solution for -8x+14=2x(4x-7) equation: 


Simplifying
-8x + 14 = 2x(4x + -7)

Reorder the terms:
14 + -8x = 2x(4x + -7)

Reorder the terms:
14 + -8x = 2x(-7 + 4x)
14 + -8x = (-7 * 2x + 4x * 2x)
14 + -8x = (-14x + 8x2)

Solving
14 + -8x = -14x + 8x2

Solving for variable 'x'.

Combine like terms: -8x + 14x = 6x
14 + 6x + -8x2 = -14x + 8x2 + 14x + -8x2

Reorder the terms:
14 + 6x + -8x2 = -14x + 14x + 8x2 + -8x2

Combine like terms: -14x + 14x = 0
14 + 6x + -8x2 = 0 + 8x2 + -8x2
14 + 6x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
14 + 6x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 3x + -4x2) = 0

Factor a trinomial.
2((7 + -4x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {1.75, -1}

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